Heterogeneity in modern datacenters is on the rise, in hardware resource characteristics, in workload characteristics, and in dynamic characteristics (e.g., a memoryresident copy of input data). As a result, which machines are assigned to a given job can have a significant impact. For example, a job may run faster on the same machine as its input data or with a given hardware accelerator, while still being runnable on other machines, albeit less efficiently. Heterogeneity takes on more complex forms as sets of resources differ in the level of performance they deliver, even if they consist of identical individual units, such as with rack-level locality. We refer to this as combinatorial heterogeneity. Mixes of jobs with strict SLOs on completion time and increasingly available runtime estimates in production datacenters deepen the challenge of matching the right resources to the right workloads at the right time. In this dissertation, we hypothesize that it is possible and beneficial to simultaneously leverage all of this information in the form of declaratively specified spacetime soft constraints. To accomplish this, we first design and develop our principal building block—a novel Space-Time Request Language (STRL). It enables the expression of jobs’ preferences and flexibility in a general, extensible way by using a declarative, composable, intuitive algebraic expression structure. Second, building on the generality of STRL, we propose an equally general STRL Compiler that automatically compiles STRL expressions into Mixed Integer Linear Programming (MILP) problems that can be aggregated and solved to maximize the overall value of shared cluster resources. These theoretical contributions form the foundation for the system we architect, called TetriSched, that instantiates our conceptual contributions: (a) declarative soft constraints, (b) space-time soft constraints, (c) combinatorial constraints, (d) orderless global scheduling, and (e) in situ preemption. We also propose a set of mechanisms that extend the scope and the practicality of TetriSched’s deployment by analyzing and improving on its scalability, enabling and studying the efficacy of preemption, and featuring a set of runtime mis-estimation handling mechanisms to address runtime prediction inaccuracy. In collaboration with Microsoft, we adapt some of these ideas as we design and implement a heterogeneity-aware resource reservation system called Aramid with support for ordinal placement preferences targeting deployment in production clusters at Microsoft scale. A combination of simulation and real cluster experiments with synthetic and production-derived workloads, a range of workload intensities, degrees of burstiness, preference strengths, and input inaccuracies support our hypothesis that leveraging space-time soft constraints (a) significantly improves scheduling quality and (b) is possible to achieve in a practical deployment.

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